The deformable object is for implantation into a surgically prepared recipient bed. The diameter of the deformable object, in its full “relaxed” state would exceed the diameter of the superficial aspect of the surgical site with a surgical pocket being created deep to the superficial aspect of the surgical site that would accommodate the full relaxed diameter of the deformable object to be implanted. A deformable object is exemplified by but not limited to a corneal lenticule for implantation. In various embodiments, the lenticule is intended for use as a lamellar graft (not full thickness) or a full thickness penetrating keratoplasty. For example, the lenticules find use for a deep anterior lamellar graft, wherein the great majority of a recipient's corneal stroma has been removed; in some cases only Descemet's membrane and its associated endothelium remains. This is commonly referred to as a deep anterior lamellar keratoplasty (DALK). The lenticules also find use for a full thickness penetrating keratoplasty, wherein the entire thickness of a recipient's cornea is removed prior to graft placement. The lenticule design, instruments and procedures enable placement of a graft that exceeds the diameter of the recipient bed and will minimize or obviate the need for sutures. Other applications include the insertion of deformable materials for use in drug delivery and transplantation of cells integrated onto the surface or embedded within a deformable matrix. A deformable matrix is exemplified by but not limited to biologic, biosynthetic and synthetic polymeric materials.